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Divisibility, Factors, GCF, Multiples, LCM, Prime, Composite, & Prime Factorization PowerPoint Presentation
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Divisibility, Factors, GCF, Multiples, LCM, Prime, Composite, & Prime Factorization. Divisibility. Divisibility – a number is divisible by another number when you divide them and there is NOT a remainder (or decimal) Calculator Time!!!!!. Divisibility con…. Example: 35 ÷ 5 = 7

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slide2

Divisibility

Divisibility – a number is divisible by another number when you divide them and there is NOT a remainder (or decimal)

Calculator Time!!!!!

slide3

Divisibility con…

Example: 35 ÷ 5 = 7

So…

35 is divisible by 5 because

there is no remainder/decimal

Example: 42 ÷ 5 = 8.4

So…

42 is NOT divisible by 5 because

there isa remainder/decimal

X

slide4

Divisibility con…

Is 45 divisible by 2, 3, 4, 5, 6, 8, 9, or 10?

45 ÷ 2 = 22.5

45 ÷ 3 = 15

45 ÷ 4 = 11.25

45 ÷ 5 = 9

45 ÷ 6 = 7.5

45 ÷ 8 = 5.625

45 ÷ 9 = 5

45 ÷ 10 = 4.5

X

So…..

45 is divisible by:

3, 5, and 9

X

X

X

X

slide5

Divisibility con…

Is 60 divisible by 2, 3, 4, 5, 6, 8, 9, or 10?

60 ÷ 2 = 30

60 ÷ 3 = 20

60 ÷ 4 = 15

60 ÷ 5 = 12

60 ÷ 6 = 10

60 ÷ 8 = 7.5

60 ÷ 9 = 6.67

60 ÷ 10 = 6

So…..

60 is divisible by:

2, 3, 4, 5, 6, and 10

X

X

slide6

Factors

Factors – the numbers we multiply together to get a product

8 x 4 = 32

Factor

Factor

Product

slide7

Factors con…

There is a specific set of factors for each number.

To find factors:

- take number and divide it by 1, then 2, then 3, then 4, etc.

- if you get a decimal – it is not a factor

- no decimal – the factor pair is the # you divided by and the answer

slide8

Factors con…

List all the factors of 48:

48 ÷ 1 = 48

48 ÷ 2 = 24

48 ÷ 3 = 16

48 ÷ 4 = 12

48 ÷ 5 = 9.6

48 ÷ 6 = 8

48 ÷ 7 = 6.86

Factors:

so

= 48

1 x 48

= 48

so

2 x 24

= 48

so

3 x 16

= 48

so

4 x 12

no

so

6 x 8

= 48

no

slide9

Factors con…

List all the factors of 36:

36 ÷ 1 = 36

36 ÷ 2 = 18

36 ÷ 3 = 12

36 ÷ 4 = 9

36 ÷ 5 = 7.2

36 ÷ 6 = 6

Factors:

so

= 36

1 x 36

= 36

so

2 x 18

= 36

so

3 x 12

= 36

so

4 x 9

no

so

6 x 6

= 36

slide10

Factors con…

List all the factors of 45:

45 ÷ 1 = 45

45 ÷ 2 = 22.5

45 ÷ 3 = 15

45 ÷ 4 = 11.25

45 ÷ 5 = 9

45 ÷ 6 = 7.5

Factors:

so

1 x 45

= 45

no

so

3 x 15

= 45

no

so

5 x 9

= 45

no

slide11

Greatest Common Factor (GCF)

Biggest Factor they have in common

Find the GCF of 36 and 24:

3624

GCF = 12

1 x 36

1 x 24

2 x 12

2 x 18

3 x 8

3 x 12

4 x 9

4 x 6

6 x 6

slide12

GCF con…

Find the GCF of 60 and 90:

6090

GCF = 30

1 x 60

1 x 90

2 x 30

2 x 45

3 x 20

3 x 30

4 x 15

5 x 18

6 x 15

5 x 12

9 x 10

6 x 10

slide13

GCF con…

Find the GCF of 45 and 72:

4572

GCF = 9

1 x 45

1 x 72

3 x 15

2 x 36

5 x 9

3 x 24

4 x 18

6 x 12

8 x 9

slide14

GCF con…

Find the GCF of 30, 45, and 70:

304570

1 x 30

1 x 45

1 x 70

2 x 15

3 x 15

2 x 35

3 x 10

5 x 9

5 x 14

5 x 6

7 x 10

GCF = 5

slide16

Prime Numbers – have only 2 factors - one and itself

  • Examples:
  • Special Case: the number 2 is the only even number that is prime!!!

2

3

5

7

11

1 x 2

1 x 3

1 x 5

1 x 7

1 x 11

slide17

Composite Numbers – have more than 2 factors

  • Examples:

4

24

12

9

1 x 4

1 x 24

1 x 12

1 x 9

2 x 2

2 x 12

2 x 6

3 x 3

3 x 8

3 x 4

1,3,9

1,2,4

4 x 6

1,2,3,4,6,12

1,2,3,4,6,8,12,24

slide18

All even numbers except the #2 are composite

  • Why?
  • All even numbers are divisible by 2
  • so 2 is going to be a factor
  • - Is the # 1 prime or composite?

1

The number 1 is neither prime nor composite – it has only one factor – the number 1

1 x 1

slide19

Practice: Tell whether each number is prime or composite

25

54

19

32

23

1 x 19

1 x 32

1 x 23

1 x 25

1 x 54

Prime

2 x 16

Prime

5 x 5

2 x 27

3 x 18

4 x 8

Composite

6 x 9

Composite

Composite

slide20

Prime Factorization – use a factor tree to factor until all that is left is prime numbers

32

Prime Factorization =

2 x 2 x 2 x 2 x 2

or

25

4

8

2

2

2

4

2

2

slide21

45

Prime Factorization =

3 x 3 x 5

or

32 x 5

5

9

3

3

slide22

36

Prime Factorization =

2 x 2 x 3 x 3

or

22 x 32

6

6

2

3

2

3

slide23

Multiples – is the product when you multiply

        • There are no set amount – there is an infinite number of multiples
        • The multiples are equal to or larger than the starting number
  • Example:
  • Multiples of 5: 5, 10, 15, 20, 25, 30…….
slide24

How do you find multiples?

    • Take the numberandmultiply it by another whole number – I like to go in orderstarting with the number 1
    • It’s like we are counting by that number
slide25

Examples:

List five multiples of the # 8

1 x 8 = 8

2 x 8 = 16

3 x 8 = 24

4 x 8 = 32

5 x 8 = 40

8, 16, 24, 32, and 40 are multiples of the number 8

slide26

Examples:

List five multiples of the # 6

1 x 6 = 6

2 x 6 = 12

3 x 6 = 18

4 x 6 = 24

5 x 6 = 30

6, 12, 18, 24, and 30 are multiples of the number 6

slide27

Examples:

List five multiples of the # 12

1 x 12 = 12

2 x 12 = 24

3 x 12 = 36

4 x 12 = 48

5 x 12 = 60

12, 24, 36, 48, and 60 are multiples of the number 12

slide28

Least Common Multiple (LCM)– smallest multiple a set of numbers have in common

  • How to find LCM:
  • 1.) Begin with the larger number
  • 2.) List 5 – 10 multiples (go in order)
  • 3.) Begin listing multiples of the other #
  • 4.) Stop when you find a multiple they have in common
  • 5.) If needed, go back and list more multiples of the first number
slide29

Example: Find the LCM of 6 and 7

Multiples of 7:

7,

14,

21,

28,

35,

42,

49,

56,

63,

70

Multiples of 6:

12,

36,

6,

18,

24,

30,

42

LCM of 6 & 7 = 42

slide30

Example: Find the LCM of 15 and 20

Multiples of 15:

15,

30,

45,

60,

75,

90

Multiples of 20:

20,

40,

60

LCM of 15 & 20 = 60

slide31

Example: Find the LCM of 5, 6, and 15

Multiples of 15:

15,

30,

45,

60,

75

Multiples of 6:

12,

6,

18,

24,

30

Multiples of 5:

10,

5,

15,

20,

25,

30

LCM of 5, 6, & 15 = 30

slide32

LCM in Word Problems:

On every third page of Sarah’s scrapbook, she has a friend’s signature. On every fourth page she has a teacher’s signature. What is the page number of the first page that will have both signatures?

How to work: find the LCM of 3 and 4

Multiples of 4:

8,

24,

4,

12,

16,

20,

28

Multiples of 3:

LCM of 3 & 4 = 12

6,

3,

9,

12,

slide33

LCM in Word Problems:

Scrapbook stickers come in packages of 10, and labels come in packages of 25. What is the least number of packages of each Sarah should buy if she needs to have an equal number of stickers and labels?

Multiples of 25:

Stickers – 5 packs

Labels – 2 packs

50,

25,

75,

100,

125

1

2

Multiples of 10:

20,

40,

10,

30,

50

1

2

3

4

5